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Question

Given that P (3, 2, –4), Q (5, 4, –6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR.

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Solution

The given points are P=( 3,2,4 ) , Q=( 5,4,6 ) and R=( 9,8,10 ) .

Let the ratio in which Q divides PR be k:1 .

According to section formula,

Q( x,y,z )=( m x 2 +n x 1 m+n , m y 2 +n y 1 m+n , m z 2 +n z 1 m+n )

Therefore, considering the x coordinate,

5= k9+13 k+1 5k+5=9k+3 9k5k=53 4k=2 k= 1 2

Therefore, the point Q=( 5,4,6 ) divides PR in the ratio 1:2 .


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